Karazin Kharkiv National University Department of Physics and Technology

Technische Universität Darmstadt Institut für Kernphysik

Design of a Shielding

for the New Focal Plane Detector System

of the Energy-Loss Spectrometer

at the S-DALINAC

Diploma Thesis

Oleksiy Burda

Darmstadt 2002

2

Abstract

The investigation of the structure of the nucleus with inelastic electron

scattering is one of the most important applications of the 130 MeV

superconducting Darmstadt electron linear accelerator S-DALINAC at the Institute

for Nuclear Physics of the Darmstadt University of Technology, Germany. In order

to carry out high resolution electron scattering experiments especially with heavy

nuclei, where the level densities are high, a new detector system is presently

developed for the so-called energy-loss spectrometer. The old scintillator system is

replaced by modern silicon-microstrip detectors.

During the experiments the detector system of the spectrometer has to be

protected against neutrons and ionising radiation produced by neighbouring

background sources by means of a passive radiation shielding. In the present work

the design of such a shielding system is developed. Estimates of the total

background produced by the typical background sources located near the

spectrometer are presented. The requirements for the new shielding are defined.

Also, the criteria of material choice for the shielding are considered. The estimates

of the shielding thickness, necessary for reducing the background level down to a

level of the proper detector operation are given. The working drawings of the

designed shielding construction system are presented.

3

Анотація

Дослідження структури ядра за допомогою непружного електронного

розсіювання є одним з найважливіших використань надпровідного

рециркулюючого лінійного прискорювача електронiв S-DALINAC на

130 МеВ в Інституті Ядерної Фізики (Дармштадський Технічний

Університет, Нiмеччина).

Для того, щоб проводити експерименти по розсіянню електронів з

високою роздільною здатністю, особливо з важкими ядрами, де щільність

рівнів є високою, детекторна система спектрометру була змінена. Стара

сцинтиляційна детекторна система була замінена на сучасні кремнієві

мікрострипові детектори.

Пiд час експерименту, детекторну систему спектрометра потрібно

захистити від нейтронів та іонізуючого випромінювання від найближчих

радіаційних джерел пасивною радіаційною захисною спорудою. Розробка

такої системи і є головною темою цієї дипломної роботи.

В рамках цієї роботи була зроблена оцінка сумарного фону біля

детекторної системи спектрометру. Були пред'явлені вимоги до нової

радіаційної захисної споруди. Також даються критерії вибору матеріалів для

захисту детекторної системи від фотонів та нейтронів. Представлені оцінки

товщини захисного матеріалу, які необхідні для зменшення фону до рівня,

який забезпечує належну роботу електронної частини детекторної системи за

допомогою коефіцієнтів десятинного ослаблення випромінювання. Також

даються креслення розробленої захисної споруди.

4

Contents

1 . Introduction.........................................................................................................5

2 . S-DALINAC and experimental facilities ............................................................6

3 . Production and attenuation of background radiation .....................................8

3.1 Bremsstrahlung yield from a target.....................................................................8

3.2 Attenuation of gamma radiation........................................................................12

3.3 Photoneutron reactions and neutron yield from a target .................................15

3.4 Slowing down and capture of neutrons.............................................................18

4 . The energy-loss spectrometer.........................................................................20

4.1 High resolution electron scattering facility........................................................20

4.2 Matrix formalism and ion-optical properties of the spectrometer ...................24

4.3 Energy-loss mode................................................................................................25

4.4 New detector system...........................................................................................27

5 . Shielding design ...............................................................................................28

5.1 Background sources and estimates of total background radiation at the

detector system ...................................................................................................28

5.1.1 Photon and neutron yields from the 70° bending magnet .......................31

5.1.2 Photon and neutron yields from the target ..............................................32

5.1.3 Photon and neutron yields from the post-target system. .........................33

5.1.4 Total instrumental background................................................................35

5.2 Requirements to the new shielding system ........................................................35

5.3 Choice of the optimal shielding materials..........................................................36

5.4 Estimates of the necessary shielding thickness..................................................38

6 . Construction of the shielding ..........................................................................40

7 . Conclusion ........................................................................................................43

8 . References ........................................................................................................44

5

1. Introduction

The investigation of the structure of the nucleus with inelastic electron

scattering is one of the most important applications of the superconducting

Darmstadt electron linear accelerator S-DALINAC at the Institute of Nuclear

Physics of the Darmstadt University of Technology. Due to its modern concept the

S-DALINAC is a high quality source of continuous electron beams with energies

up to 130 MeV. For momentum analysis of the scattered on the target electrons in

nuclear physics experiments the so-called QCLAM spectrometer is used. Due to its

large solid angle and momentum acceptance this spectrometer is well suited for

(e,e′x) coincidence and 180° scattering experiments [1-3].

Additionally, a spectrometer for high resolution (e,e′) experiments which

was already used with the old normal-conducting accelerator DALINAC [4-7] is

available. This spectrometer is operated in a so-called “energy-loss” mode. The

main advantage of this mode is that the resolution of the electron scattering

experiment does not depend on the energy spread of the primary electron beam. In

order to carry out high resolution electron scattering experiments especially with

heavy nuclei, where the level densities are high, a new detector system is presently

developed at the spectrometer [8]. The old scintillator system is replaced by a

modern silicon microstrip detector.

During the experiments the detector system of the spectrometer has to be

protected against neutrons and ionising radiation by the radiation shielding. The

new detector system requires a new shielding design. Development, construction

and installation are the aim of this diploma thesis.

6

2. S-DALINAC and experimental facilities

The S-DALINAC was constructed at the Institute for Nuclear Physics of

the Darmstadt University of Technology [9]. It became the first superconducting

continuous-wave linear accelerator of electrons in Europe. Since 1991 the

S-DALINAC delivers electron beams with the maximum energy of 120 MeV and

currents of up to 60 µA for a wide range of experiments. The layout of the

S-DALINAC is shown in Fig. 1.

5 m

A rea

25 0 ke V

P reacce le ra to rC h oppe rP rebu ncher10 M eV In jec tor

E xperim enta l

40 M eV L in ac

1s t R ec ircu la tion U n du la to r O ptica l C av ity 2n d R ec ircu la tion

To E xperim e nta lH a ll

To O p tics La b

Fig. 1: Schematic layout of the S-DALINAC.

The electrons are emitted by a thermionic gun and then accelerated

electrostatically to an energy of 250 keV. The required time structure of the

electron beam for radio-frequency acceleration in a 3 GHz field is created by a

chopper/prebuncher system operating at room temperature. The superconducting

injector linac consists of one 2-cell, one 5-cell, and two standard 20-cell niobium

cavities cooled to 2 K by liquid helium. The beam leaving the injector has an

energy up to 10 MeV and can either be used for radiation physics experiments or

for nuclear resonance fluorescence experiments. Alternatively, it can be bent by

1800 and injected into the main accelerator section. This superconducting linac has

7

eight 20-cell cavities which provide an energy gain of up to 40 MeV. After passing

through the main linac the electron beam may be extracted to the experimental hall

or it can be recirculated and reinjected one or two times. Additionally, in the first

recirculation beam-line an infrared Free Electron Laser (FEL) is located. After

three passes the electron beam with a maximum energy of up to 130 MeV is

delivered to several experimental facilities, schematically shown in Fig. 2.

Fig. 2: Experimental facilities at the S-DALINAC.

1 - channeling radiation and (γ,γ ′) experiments, 2 - Free Electron Laser, 3 - high

energy radiation physics, 4 - compton scattering off nucleons 5 - (e,e') at 180° and

(e,e'x) experiments, 6 - (e,e')-experiments, 7 - optic experiments.

A wide range of electron scattering experiments is carried out using the

QCLAM spectrometer (Pos. 5) and a high resolution energy-loss facility with a

magic-angle spectrometer (Pos. 6). The QCLAM-spectrometer has a large angular

and momentum acceptance and is used for (e,e′x) coincidence and (e,e′) at 180°

experiments. The magic-angle spectrometer operates in the so-called “energy-loss”

mode that enables to perform high resolution (e,e′) experiments independently of

the energy spread of the electron beam.

8

3. Production and attenuation of background radiation

The main secondary effects produced by the passage of charged particles

through matter are the excitation and ionization of atoms, and emission of photons

and ejection of neutrons from nuclei. The first two phenomena can be considered

as the result of a direct interaction between the primary particles and atomic

electrons, and may be referred to as non-radiative collision processes, or, shortly,

as collision processes. The emission of photons is caused by the deceleration of the

primary particle in the Coulomb field of the nucleus. This process may be denoted

as a radiative collision process, or, shortly, as a radiation process.

Therefore, the total energy loss of electrons is composed of two parts

collradtot dx

dE

dx

dE

dx

dE

+

=

. (1)

Photons are radiated from any object struck by the primary electrons and

form an external secondary beam. In a situation where photons are incident on

matter there are three main processes: photoelectric effect, Compton effect, and

pair production. The probability of electron-positron pair production rises with

increasing photon energy and becomes important at energies above about 5 MeV

in high-Z materials. Thus, the phenomenon of the electromagnetic shower or

cascade occurs [10]. At high energies this phenomenon plays a dominant role in

the description of the energy loss. Furthermore, background neutrons can be

produced via photonuclear reactions.

In this section all these processes will be described more detailed.

3.1 Bremsstrahlung yield from a target

When a swiftly moving charged particle of mass m and charge z passes

close to a nucleus of charge Z, it experiences a Coulomb force proportional to z⋅Z

and consequently undergoes an acceleration proportional to z⋅Z/m. According to

9

classical physics, an accelerated charge radiates electromagnetic energy at a rate

proportional to z2⋅Z2/m2. The proportionality to the square of the atomic number

means that the loss of energy by radiation should be much more important in heavy

elements than in light ones, while the inverse proportionality to the square of mass

implies that light particles should radiate much more readily than heavy ones.

Consequently, radiation as an energy loss mechanism is usually significant for

electrons only.

The bremsstrahlung-energy spectrum extends from zero to the full initial

energy of the electrons. Typical distributions for a number of electron energies in

platinum (Z=78) are shown in Fig. 3 [11].

Relative

inte

nsity

Eγ E0

Fig. 3: Bremsstrahlung spectrum for various electron energies in platinum [11].

The average opening angle of the emission cone of bremsstrahlung photons

at relativistic energies is given approximately by the well-known formula

0

2

E

mc≈θ (2)

where E0 is the initial energy of the electron.

10

As pointed out above, the rate of energy loss by radiation is roughly

proportional to the square of the atomic number of the stopping material. It also

increases rapidly with the energy, being negligible below 100 keV and rising to

values greater than the rate of loss by collision at energies between 10 and 100

MeV, depending on the material. In the relativistic limit 0E • 312137 −Zmc , where the

screening of the nuclear charge by the atomic electrons is complete, the rate of loss

is given by [12]

)183ln()1(4 310

20

−+=

− ZEnrZZ

dx

dE

rad

α , (3)

where n is the number of target atoms per cm3, α is the fine structure constant, and

r0 is the classical electron radius.

The bremsstrahlung energy loss is proportional to the initial energy of

electrons as shown in Fig. 3. The energy at which the losses due to collision and

bremsstrahlung for electrons are the same

coll

c

rad

c

dx

dE

dx

dE

=

(4)

is called critical energy Ec. Above this energy radiation loss will dominate over

collision-ionization losses. An approximate formula for Ec is given by [13]

[ ]MeVZ

Ec 24.1

800

+= . (5)

The ratio of the radiation loss to the collision loss at the energy E0 is about

( )( ) 2

0

1600 mc

ZE

dxdE

dxdE

coll

rad

⋅⋅≈ . (6)

It can be seen from Eq. (6) that, whereas in graphite (Z = 6) the radiation loss

becomes comparable to the collision loss only at energies above 100 MeV, in lead

(Z = 82) these two are equal already at about 10 MeV.

Above the critical energy the electrons will lose their energy according to

−⋅=

radL

xEE exp0 , (7)

where x is the distance traveled and Lrad is the radiation length. For quick

calculations, the following convenient expression for Lrad can be used [12]

11

( )

+

⋅=2287ln)1(

4.716

cm

g

ZZZ

ALrad , (8)

where A is the mass number of the target.

Using the atomic model of Thomas and Fermi, Schiff [14] obtained the

following expression for the bremsstrahlung cross section for full screening and

relativistic energies of the incident electrons

( ) ( )

( )

+−+

−+

−−

⋅

−×

×

+−

−+

−⋅

+⋅

−⋅⋅

+=

22

2

0

0

0

02

0

00

22

2

0

0

0

0220

02

00

1

162

2

1)(2ln

1

4

1137

)1(8),(

x

x

E

EE

EE

E

Ecm

EEE

x

x

E

EE

EE

E

x

xdx

E

EE

E

dErZZEd

γ

γγ

γ

γ

γ

γ

γ

γγγ θσ

(9)

Here, θ⋅=2

0

0

cm

Ex is the reduced photon emission angle.

The total photon yield in the thin-target approximation can be expressed as

follows

∫ ∫−

⋅⋅⋅=

20 0

0

0

0

),(

mcE

ea EdtN

A

NY θσ γγ

θ

γ , (10)

where Na is Avogadro’s number, Ne is the number of electrons hitting the target, t

is the target areal density.

The radiation yield for electrons stopped in various media is shown in

Fig. 4 [15].

12

Rad

iation

yield

(a.u.)

E (MeV)0

Fig. 4: The radiation yield for electrons stopped in various media [15].

3.2 Attenuation of gamma radiation

As was mentioned above, high energy photons traversing matter undergoes

the following secondary processes:

Photoelectric effect: absorption by an atom accompanied by the emission

of a high energy electron from the atom. Though the photoelectric effect becomes

less and less important with increasing photon energy, even at MeV energies the

dependence of the cross section per atom, phσ , scales with Z5. Clearly, higher Z

materials are most favoured for photoelectric absorption.

Compton effect: scattering of photons on free electrons. In this case the

cross-section cσ depends linearly on atomic number Z.

Pair production, i.e., transformation of photon energy into an electron and

a positron. In this case the cross section per atom is proportional to Z3.

The energy dependences of these processes for lead are shown in Fig. 5.

13

Cross

section

(barns/atom)

Photoelectric effect

Compton effect

Pair production

Total

L-edges

K-edge

E (MeV)γ

Fig. 5: The photon absorption cross section for lead [12].

The intensity of a narrow photon beam passing through a material with a

thickness t, reduces exponentially

ttoteII µ−⋅= 0 , (11)

where I0 is the initial intensity of the monoenergetic photon flux interacting with

matter, and µtot represents the total linear attenuation coefficient, which is given by

)( paircphA

tot A

N σσσρµ ++⋅= . (12)

Here σph, σc, and σpair are the cross sections for the photoelectric effect, Compton

scattering, and pair production, respectively, and ρ is the density of the material.

For compounds and mixtures the total attenuation coefficient may be

calculated using Bragg’s rule

14

K++=2

22

1

11 ρ

µωρµω

ρµ , (13)

where ωi is the weight fraction of each element in the compound. The linear

absorption coefficient µ is proportional to the density of the absorbing material. It

is often more convenient to deal with the mass attenuation coefficient, µ/ρ which is

approximately independent of the material properties. It is a function of the photon

energy but not of the radiation intensity or material thickness.

In practice and in the discussions presented in this diploma thesis the

concept of tenth-value layers (TVL) is used for estimates of the shielding thickness

against bremsstrahlung and neutrons. A TVL is defined as the thickness of

absorber that will reduce the intensity of a narrow beam of the radiation by a factor

of ten. When the attenuation is exponential, the tenth-value layer is given by

=

2

10ln

cm

gTVL

tot

ρµ

. (14)

The simple exponential attenuation described by Eq. (11) is observed only for a

monoenenergetic photon beam. When photons of more than one energy are

present, the net attenuation coefficient is determined by weighting with the

spectrum of photon energies. However, for practical purposes the TVL originally

developed for dose considerations remains a useful approximation for particle

intensities as well.

The photon and neutron tenth-value layers of various shielding materials

are given in Tab. 1. One can see that lead is the most effective attenuator of

photons and polyethylene is that of neutrons.

15

Tab. 1: The photon and neutron tenth-value layers of different shielding materials [16-18].

Material Density [g/cm3]

TVLγ

[cm] TVLn

[cm]

Pb 11.35 5 33

Fe 7.87 10 30

Concrete 2.35 48 40

Polyethylene 0.93 173 16

3.3 Photoneutron reactions and neutron yield from a target

Above a threshold energy which varies from about 10 to 19 MeV for light

nuclei and from 6 to 8 MeV for heavy nuclei, neutron production will take place in

any material hit by an electron or bremsstrahlung beam. The produced neutrons

may present a radiation hazard by themselves and are also a source of induced

activity.

Between the threshold and approximately 30 MeV, neutron production

results primary from a process known as excitation of the giant dipole resonance

(GDR). The physical mechanism can be described as one in which the electric field

of a photon transfers its energy to the nucleus by inducing an oscillation in which

the protons as a group move oppositely to the neutrons as a group. The cross

section of GDR has a maximum at photon energies of approximately 20-23 MeV

for light nuclei (A ≤ 40), and 13-18 MeV for medium and heavy nuclei. For A ≥

40, the energy of the peak is approximately given by

MeVAE 310 80 −⋅=γ . (15)

This phenomenon occurs in all nuclei (except 1H). The width of this peak varies

between 3 MeV (heavy nuclei) and 10 MeV (light nuclei).

In the semiclassical theory of the interaction of photons with nuclei, the

shape of a resonance in the absorption cross section as a function of the photon

energy γE has the form of a Lorenz distribution [19]

16

22

02

max

1

)(

Γ⋅

−+

=

γ

γγ

γσσ

E

EEEn , (16)

where maxσ is the maximum cross section (in barns) of the giant resonance, 0γE

and Γ are the photon energy for maxσ and full width at half maximum of the cross

section in MeV, respectively. The absorption cross section of 208Pb as a function of

the photon energy is shown in Fig. 6 [20, 21].

0 10 20 30 400

100

200

300

400

500σmax= 490 mb

E γ 0= 13.46 MeVE

γ th= 7.37 MeV

Γ = 3.9 MeV

σ n

(E

γ)

(mb)

Eγ

(MeV)

Fig. 6: Photoneutron cross section of 208Pb as a function of photon energy [20, 21].

The neutron yield from bremsstrahlung in the thin-target approximation can

be obtained from the following expression

γγ

γγγ

γ

γ

σ dEdE

EdYE

A

NtY

E

E

na

n

th

)()(

max

⋅⋅⋅= ∫ , (17)

where thEγ , maxγE are the threshold energy and maximum photon energy for giant

resonance.

The typical situation at electron accelerators corresponds to thick targets. In

this case one has to perform numerical simulations. Neutron yields from semi-

17

infinite targets per unit electron beam power are plotted in Fig. 7 as a function of

the electron beam energy [22].

The produced neutrons exhibit a roughly isotropic angular distribution with

a Maxwellian energy distribution

TEn

n

n neT

E

dE

d −=Υ

2, (18)

where T is a parameter characteristic of the target nucleus ( e.g. T = 0.98 MeV for

lead).

Y(neutronss

kW

)n

-1

-1

E (MeV)0

Fig. 7: Neutron yields from semi-infinite targets per kW of electron power as a

function of electron beam energy, disregarding target self-shielding [22].

18

3.4 Slowing down and capture of neutrons

Passing through matter, the neutrons undergo a variety of nuclear processes

depending on their energy. Among them are:

1. Elastic scattering from nuclei, i.e. reactions A(n,n)A. This is the most

important mechanism of energy loss for neutrons in the MeV region. The

maximum energy that can be transferred to a nucleus of mass number A by a

neutron of energy En is given by

2

max )1(

4

+=

∆A

A

E

E

n, (19)

where ∆E is the energy lost by a neutron, and En is the initial neutron energy.

The average loss of energy in an elastic collision is the largest when the

neutron is scattered off a hydrogen nucleus [12]. It is found that the average

logarithmic energy loss suffered by a neutron of initial energy En in a collision

with nucleus of mass number A is

+−−+=−=

1

1ln

2

)1(1lnln

2

A

A

A

AEEnξ . (20)

This value does not depend upon the initial neutron energy and is a constant for a

given material. Therefore, this quantity is convenient for estimating the moderating

ability of a material.

The average number of collisions needed to reduce the neutron energy from

an initial value E0 to a lower energy E is given by

ξ

)ln( EEn n= . (21)

Thus, e.g. the average number of collisions necessary to reduce the energy of the

neutron from 2 MeV down to 0.025 eV (thermal energy) in hydrogen is only 18, in

graphite is over 100, and in lead is already about 2000.

2. Inelastic scattering, i.e. A(n,n′)A*, A(n,2n′)B, etc. In this reaction the nucleus

is left in an excited state which decays by gamma rays or some particle emission (if

19

energetically allowed). In order for the inelastic scattering to occur, the neutron

must have sufficient energy to excite the nucleus, usually of the order of 1 MeV or

higher. Below this energy threshold, only elastic scattering may occur.

3. Radiative neutron capture, i.e. a reaction n + (Z, A)→ γ + (Z, A+1). In

general, the cross section for neutron capture goes approximately as ≈ υ1 , where

υ is the velocity of the neutron. Absorption is most likely, therefore, at low

energies. Extremely high thermal neutron absorption cross sections are provided

e.g. by boron, cadmium and gadolinium.

In the design of a passive radiation shielding it is necessary to take into

account the fact that neutron elastic scattering and neutron capture are generally

accompanied by the production of secondary gamma rays. Therefore, the shielding

against neutrons is placed first to the background source and the one against

photons is placed second closer to the protected object.

The total probability for a neutron to interact with matter is given by the

sum of the individual cross section, i.e.

captureinelasticelastictot σσσσ ++= . (22)

In analogy to photons, then, a collimated beam of neutrons passing through

matter will be exponentially attenuated

tn toteII ⋅⋅−= σ0 . (23)

20

4. The energy-loss spectrometer

4.1 High resolution electron scattering facility

The layout of the high resolution energy-loss system is shown in Fig. 8.

This system allows the operation of the spectrometer in the so-called energy-loss

mode. It permits measurements where the resolution of electron scattering

experiments does not depend on the energy spread of the electron beam.

tothe

QCLA

M

spectrometer

5 4

1

3

67

8

2

e beam from

S-DALINAC

Fig. 8: High resolution energy-loss system.

Î focussing quadrupoles, Ï energy defining slit, Ð 70° bending magnets, Ñ

“rotator”, Ò focussing quadrupole triplet, Ó refocussing quadrupole doublet, Ô

Faraday cup, Õ energy-loss spectrometer.

The system consists of six quadrupoles (Pos. 1) and two 70° bending

magnets (Pos. 2) which form a momentum analyzing system with energy defining

slits (Pos. 3) in the symmetry plane between these magnets. A set of five

quadrupoles called “rotator” (Pos. 4), is used to turn at 90° the dispersion plane in

the energy-loss mode of operation, and the quadrupole triplet (Pos. 5) focusses the

21

beam onto the target. A quadrupole doublet (Pos. 6) behind the target reduces the

beam divergence due to multiple scattering and delivers it to a Faraday cup (Pos. 7)

which simultaneously serves as current monitor. The scattered electrons are

momentum analyzed in a high resolution magic-angle spectrometer (Pos. 8).

The energy-loss spectrometer is shown in Fig. 9. The electron beam from

the accelerator hits the target which is placed inside the scattering chamber at the

pivot-point of the spectrometer (Pos. 1). The scattered electrons pass the

spectrometer entrance slit defining the accepted solid angle Ω, and are deflected by

the dipole magnet (Pos. 2) to an angle of 38π = 169.7° (this angle is called

“magic” for reasons discussed in Sect. 4.3). Then electrons come out through the

output vacuum chamber (Pos. 4), having been focussed in the focal plane where

the new detector system will be located [4].

22

2

4

e

3

1

Fig. 9: The 169.7° spectrometer without detector system.

1 - scattering chamber, 2 - dipole magnet, 3 - paraffin and lead

shielding, 4 - vacuum chamber.

23

The main parameters of the spectrometer are given in Tab. 2.

Tab. 2: Parameters of the energy-loss spectrometer.

Electron energy range 18 - 120 MeV

Angle range 25°-165°

Deflection angle 169.7° ± 0.1°

Radius of central trajectory 1.00 m

Solid angle acceptance 5 msr

Dispersion 4 cm /%

Field strength 0.6 - 4.0 kG

Weight

spectrometer 17 t

shielding (safe load) 10 t

24

4.2 Matrix formalism and ion-optical properties of the spectrometer

In order to describe the behavior of charged particles passing through one

or more ion-optical devices the concept of transfer coefficients is used [23]. The

box in Fig. 10 represents any ion-optical transfer system consisting of magnetic

dipoles, quadrupoles etc. A particle is assumed to be emitted from (or passing

through) points X1, Y1 in the plane Z1 = 0. After having transversed the system, it

will be detected at position X2, Y2 in the plane Z2 = 0. The direction of the particle

before entering the system is specified by the angles θ1 and Ф1 defined in the

figure. A reference momentum p0 is assumed, and the deviation from this

momentum is given as δ = ∆ p / p0. For simplicity, it is assumed that the system is

mechanically symmetric about the XZ - plane and that for Y = 0 the magnetic field

is perpendicular to this symmetry plane. At the energy-loss spectrometer it should

be the symmetry plane of the dipole magnet.

Fig. 10: Illustration of the coordinates for a calculation of a magneti c deflection system.

The electron beam position at the exit is a function of the position and

direction at the entrance and of the momentum. Thus

),,,,( 11112 δθ ФYXfX = (24)

25

with similar expressions for θ2, Y2, and Ф2. The exit coordinate system is chosen

such that a particle with momentum p0 entering along the Z1 axis exits along Z2.

Then Eq. (24) can be expressed as a Taylor expansion in X1, θ1, Y1, Ф1, and δ :

.)()()(

)()()()(

)()()()()/(

21

211

21

2

2211

21

211

21

2112

termsorderhigherФФXФYYФXYYX

XXXXXX

XXXXXXXXXXXX

++++

+++++

+++++=

δδδθθδδδθθ

θθδδθθ

(25)

The factor (X / X), called a transfer coefficient, is actually the first-order

derivative ∂ X2 / ∂ X1. Similarly, the term (X / θ ) is equal to ∂ X2 / ∂ θ1, etc. The

term (X / X) is the magnification of the system in the X direction and (X / δ ) is the

dispersion. This measures the displacement in the X direction at the exit per unit

change in δ.

4.3 Energy-loss mode

In the energy-loss mode the spectrometer is used in conjunction with the

beam transport system (see Fig. 11). Its basic principle is to match the dispersion

of this system to that of the spectrometer such that the entire apparatus (starting at

the accelerator exit) is non-dispersive in the spectrometer focal plane. This makes

the system sensitive only to the energy loss in the target and independent of the

momentum spread of the beam.

The electron beam is projected on the target by the beam transport system

described in Sect. 4.1 at different spots. The distance between them is defined by

the beam energy spread δE. If the dispersion of the beam transport system and that

of the spectrometer are matched then the electron beam is focussed onto the focal

plane in one spot. If the electrons lose their energy by passing the target the spot in

the focal plane is displaced by the distance ∆ x determined by the energy-loss value

∆E of electrons in the target.

26

Focal plane

Dipole magn

Beam transport system

E + E0 δ

E - E0 δ

E0

Target

e beam

the accelerator

Fig. 11: Operation principle of the energy-loss mode.

The magnetic field in the spectrometer midplane can be described by the

expansion

[ ]K+−+−= 30

2000 )()()(1 RXRXRXnBBy γβ (26)

with X = R - R0 , where X represents the radial distance and R0 the radius of the

central trajectory, and n, β, γ are the first, second, and third derivatives of the

magnetic field B with respect to R, respectively. Since n = 0.5 is necessary to

obtain double focussing, only β and γ are optional. To facilitate manufacturing

conical pole shoe faces yielding β = 0.25 and γ = 0.125 were chosen. The

deflection angle of 169.7°, together with the straight yoke edges at entrance and

exit, is chosen such that the second order error ( X / θ 2) vanishes for all object

distances. The error ( X / θδ ) is eliminated by tilting the focal plane with respect to

the central trajectory by an angle α (see Fig. 12) given by

)(

))((tan

θδδθθα

X

X−= . (27)

27

In the present system α ≈ 35°.

Thus there is the possibility with a peak beam currents of up to 20 µA and

electron energies of up to 120 MeV to carry out electron scattering experiments

with an energy resolution of about 30 keV [24].

4.4 New detector system

Recently, a new focal plane detector system based on silicon microstrip

detectors was developed for the energy-loss spectrometer [8]. The main advantages

of these detectors are that they can be able to work with very high count rates, have

very high resolution and an easy mechanical setup. The detector system for the

scattered electrons consists of silicon microstrip detectors (4×96 strips) and a

trigger detector (see Fig. 12).

eα

10 mm thick st e

of the spectrometer

300 mm thick paraffin

100 mm thick lead

10 mm thick st e e

200 mm thick

borated polyethylene

Plastic scintillato

Silicon microstrip

detectors

Cherenkovcounter

Fig. 12: New detector system with new shielding.

28

A plastic scintillator and a large Cherenkov counter serve as a trigger for

background suppression. The spatial resolution of the semiconductor micro-strips

is 0.5 mm which corresponds to EE∆ = 3×10-5. For comparison, at the QCLAM

spectrometer which is operated in the conventional mode, in spite of the fact that

intrinsic resolution of the Multiwire Drift Chambers (MWDC) which serve as focal

plane detectors at the spectrometer is estimated to be 2×10-4, energy resolution

under typical experimental conditions is about 8×10-4-1×10-3 and is basically

determined by the energy spread of the beam and energy loss of electrons in the

target [25].

5. Shielding design

In order to determine the necessary amount of shielding material some

estimates of the background radiation around the detector system were made. This

defines together with conditions which are necessary for proper operation of the

detector system the layout described below.

5.1 Background sources and estimates of total background radiation

at the detector system

The main background sources close to the spectrometer are shown in

Fig. 13. These are the 700 bending magnet (Pos. 1), the target (Pos. 2), the post-

target system (Pos. 3) consisting of the beam pipe having 20 cm in diameter and

two focussing quadrupole magnets, and further downstream the Faraday cup

(Pos. 4).

29

tothe

QCLA

M

spectrometer

4 31

2

e beam from

S-DALINAC

Fig. 13: Background sources close to the magic-angle spectrometer.

Î 70° bending magnet, Ï scattering chamber, Ð post-target system,

Ñ Faraday cup.

The Faraday cup is separated from the spectrometer by a concrete wall

which is about 1 m in thickness followed by about a 30 cm thick paraffin brick

wall. The post-target system is enclosed in an about 30 cm thick paraffin layer

covered by about 20 cm thick borated polyethylene plates. With respect to the

detector position between the 70° bending magnet and the spectrometer there is

about 1 m of concrete. Previous experiments at the QCLAM spectrometer, where

an identical beam stopper is used, have shown that the background from the

Faraday cup can be neglected. Thus, it was necessary to estimate the total photon

and neutron fluxes near the detector system created by the 70° bending magnet, the

target and the post-target system.

To treat the problem of the estimates for the secondary particles yield

analytically it is necessary to make the following simplifications:

30

1. The thin target approximation will be used instead of the thick target

approximation for the calculation of the bremsstrahlung yield. This will result

in an overestimate of yields because the yield scales with E0.

2. The yield of bremsstrahlung photons at an angle of 10° is estimated using the

relation constE =⋅ 00θ with respect to the detector position solid angle that

results in [26]

110)0(

)10( −≈°°

atY

atY

γ

γ

and at an angle of 90° by using the thick-target dose relation [26]

310)0(

)90( −≈°°

atY

atY

γ

γ .

3. Though the range of 130 MeV electrons is about 26 g/cm2 [15], the effective

range is assumed to be about 5 g/cm2 because γ - radiation is reduced due to

slowing down of electrons. Additionally the conversion efficiency to radiation

is only about 50 %, as the radiation length Lrad in iron is about 14 g/cm2 [22].

These simplifying assumptions are chosen conservatively, i.e. rather over- than

underestimating particle fluxes.

31

5.1.1 Photon and neutron yields from the 70° bending magnet

It is assumed that traversing the magnet, 10 % of the total electron beam are lost

and hit the magnet wall passing a depth of 5 g/cm2.

Tab. 3: Input parameters for estimating the photon and neutron yields

from the 70° bending magnet.

Electron energy 120 MeV

Electron current 2 µA

Target steel

Target thickness 5 g/cm2

σmax 490 barns

Eγ 0 13.46 MeV

Γ 3.9 MeV

Eγ th 7.37 MeV

Eγ max 30 MeV

The number of photons per second produced in the bending magnet that

reach the detector system can be written in the following way

⋅−⋅∆Ω⋅°== 10lnexp4

)10( 0concrete

concrete

TVL

tYY

πθγγ , (28)

where )10( °=θγY is the total photon yield in the direction of the detector system.

This is located at the angle of 10° with respect to the 70° bending magnet, ∆Ω is

the solid angle of detector system, tconcrete is the thickness of concrete shielding.

The value of )10( °=θγY was calculated using Eq. (10) and the data from Tab. 3.

The number of neutrons reaching the detector system can be estimated by

the following expression

32

⋅−⋅∆Ω⋅= 10lnexp4 concrete

concretetotnn TVL

tYY

π, (29)

where totnY is the total neutron yield. The total neutron yield totnY was calculated

using Eqs. (10, 16, 17) and the data given in Tab. 3.

5.1.2 Photon and neutron yields from the target

To estimate the contribution to background resulting from the target it is

necessary to choose a case with maximum photon and neutron yields. Additionally

it is necessary to take such real input parameters giving maximum possible yields

of secondary particles from a target. A 208Pb target with a thickness of 20 mg/cm2

satisfies these requirements.

The detector system is located approximately at an angle of 90° relative to

the beam axis and the target itself. The produced neutrons exhibit a roughly

isotropic angular distribution and possess a Maxwellian energy distribution [see

Eq. (18)].

Tab. 4: Input parameters for estimates of the photon and neutron yields

for the target.

Electron energy 120 MeV

Electron current 20 µA

Target 208Pb

Target thickness 20 mg/cm2

σmax 490 barns

Eγ 0 13.46 MeV

Γ 3.9 MeV

Eγ th 7.37 MeV

Eγ max 30 MeV

33

The number of photons incident on the detector system will be approximately

⋅

+−⋅∆Ω⋅°== 10lnexp

4)90( 0

steel

platform

steel

chamber

TVL

t

TVL

tYY

πθγγ , (30)

where )90( 0 °=θγY is the total photon yield for the target at the angle of 90°, tchamber

and tplatform are the thickness of the lid of the scattering chamber and the

spectrometer platform, respectively. The value of )90( 0 °=θγY was calculated using

Eq. (10) and the data given in Tab. 4.

The amount of neutrons reaching the detector system is given by the

expression

π4

∆Ω⋅= totnn YY , (31)

where totnY is the total neutron yield from the 208Pb target which is expressed

using Eqs. (10, 16, 17) and the data from Tab. 4.

5.1.3 Photon and neutron yields from the post-target system.

Here it is assumed that after the electron beam passes the target, only 1 % of the

electrons hits on the scattering chamber walls which again serve as an infinitely

thick target as in the case discussed in Section 5.1.2.

34

Tab. 5: Input parameters for estimating the photon and neutron yields

from the post-target system.

Electron energy 120 MeV

Electron current 0.2 µA

Target steel

Thickness 5 g/cm2

σmax 490 barns

Eγ 0 13.46 MeV

Γ 3.9 MeV

Eγ th 7.37 MeV

Eγ max 30 MeV

The number of photons that reach the detector system will be

approximately

π

θγγ 4)90( 0

∆Ω⋅°== YY , (32)

where )90( 0 °=θγY is the total photon yield which is estimated using Eq. (10) with

the input parameters given in Tab. 5.

The amount of neutrons reaching the detector system is given by the

expression

⋅−⋅∆Ω⋅= 10lnexp4 paraffin

paraffintotnn TVL

tYY

π, (33)

where totnY is the total neutron yield which is estimated using the Eqs. (10, 16, 17)

and input parameters given in Tab. 5.

35

5.1.4 Total instrumental background

All the results of background yield estimates without a detector shielding are

summarized in Tab. 6.

Tab. 6: Results of background yield estimates without a detector shielding.

Background Source Photon Yield [s-1]

Neutron Yield [s-1]

70° bending magnet 8.0×104 2.8×102

Target 2.5×104 4.3×102

Post-target system 2.3×105 2.1×104

TOTAL 3.4×105 2.2×104

5.2 Requirements to the new shielding system

The new shielding system should satisfy the following requirements:

1. It should ensure attenuation of background radiation necessary for a proper

detector operation within a high signal-to-noise ratio.

2. Assembling and disassembling should be easy to allow simple access to the

detectors for maintenance and testing.

3. The total weight should be less than 10 tons because this is the safe load on the

spectrometer platform.

4. The weight of individual pieces should not exceed 5 tons which is the

maximum capacity of the crane available in the experimental hall.

36

5.3 Choice of the optimal shielding materials

In principle, any material can be used for radiation shielding if employed in

a thickness sufficient to attenuate the radiation to the required level. The choice of

the shield material depends on a number of factors, such as costs, final desired

attenuated radiation levels, resistance to radiation damages, required thickness and

weight, multiple use considerations, permanence of shielding, and availability.

It was already mentioned, that the attenuation of gamma rays and x-rays

depends on the density of the shielding material; a dense shield material with a

higher atomic number is a better attenuator of photons. Lead shields are frequently

used where space is limited or where a compact area of absorbers is required. It is

recognized that lead is not the densest element (e.g., tantalum, tungsten, and

thorium are higher on the density scale), but lead is readily available, has a high

degree of flexibility in an application, is easily fabricated and has by far the lowest

cost of these materials.

The lead used as shielding material is usually an alloy with a few per cent

of antimony which unfortunately is activated easily by (γ,n), and (n,γ) reactions.

However, the resulting background rates can be neglected with respect to the

results of Tab. 6.

In choosing the material for the shielding against neutrons it is necessary to

take into account the following fundamental neutron interactions processes:

1. (n,γ) capture dominant at thermal energies

2. resonant capture at keV-MeV energies

3. inelastic scattering important at MeV energies

4. elastic scattering important at MeV energies

5. nuclear reactions like (n,p), (n,α)

6. fission (not relevant here).

An ideal neutron shielding material is a combination of elements, which

maximises the effects of these interaction processes over a wide range of neutron

37

energies. Thus, to make an efficient shield against neutrons it is necessary to use a

mixture which contains

1. hydrogen, to slow down the fast- and intermediate-energy neutron by inelastic

scattering,

2. material with a sufficiently high thermal neutron capture cross section in order

to capture the neutrons efficiently after they slowed down. If possible, this

material should not emit a very penetrating gamma ray after neutron capture;

both, lithium and boron fulfil these requirements best,

3. high density elements to absorb the gamma rays formed in neutron capture and

neutron inelastic scattering, and also to make the shield compact.

When taking into account the physical properties, easy fabrication and

costs, polyethylene with 5-10 % of boron admixture is an optimal choice for

neutron shielding in cases where a free space is limited.

In general, concrete is favoured for shielding around accelerators because

cost effectiveness. However, this kind of shielding requires space and therefore is

not applicable here.

The radiative fields of gammas and neutrons at an electron accelerator

exibit a complex energy distribution. The most important aspects can be

summarized by considering the fast neutrons in the MeV range, thermal and

epithermal neutrons, primary and secondary gammas. There are different types of

shielding for each type of radiation.

Shielding for fast neutrons up to about 10 MeV is accomplished most

efficiently by the use of elastic scattering on hydrogen nuclei. Hydrogen will also

capture low energy neutrons, but this results in the undesirable emission of very

penetrating secondary gamma rays. It is beneficial, therefore, to introduce an

additional element which, even in low concentrations, is many orders of magnitude

more effective than hydrogen in absorbing the thermal neutrons, but which emits

no secondary radiations. Boron or lithium are elements with the most appropriate

properties, and are most commonly used.

38

Thermal neutrons are neutrons in thermal equilibrium with their

surroundings. Typical scattering of thermal neutrons does not generally change

their kinetic energy. The upper limit of the thermal energy range is often taken as

the cadmium cut-off energy of 500 keV. Thermal neutrons can be virtually

eliminated by the presence of high thermal neutron cross-section materials such as

boron, lithium, or cadmium.

Secondary gamma rays, with an energy of 2.2 MeV are arisen as a result of

the capture of thermal neutrons by hydrogen. These capture gamma rays can be

minimized by adding boron or lithium. Gamma rays resulting e.g. from capture of

neutrons by boron have an energy of only 0.42 MeV which reduces the overall

dosage considerably. Other materials should be avoided because they produce high

energy γ - rays in the range of 3-5 MeV.

5.4 Estimates of the necessary shielding thickness

For a proper detector operation, the photon and neutron fluxes should be

reduced as much as possible. In the development of the new shielding it is

necessary to find a compromise between quality, cost and weight of the new

shielding. The neutron yields presented in Tab. 7 are generally much lower than

the photon yields. Thus, for an estimate it is necessary first to define the admissible

photon flux through the detector system. It is defined by the maximum detector

electronic read-out rate, the semiconductor detector charge saturation and the

necessary signal-to-noise ratio.

As a starting point the experience gained at the QCLAM spectrometer can

be used [27]. There a shielding of 10 cm thick lead and 20 cm thick borated

polyethylene is employed which reduces the photon and neutron yields by a factor

of about 110 and 20, respectively (see Tab. 1).

39

Tab. 7: Results of background estimates with a detector shielding.

Background Source Photon Yield [s-1]

Neutron Yield [s-1]

70° bending magnet 7.2×102 14

Target 2.3×102 22

Post-target system 2.1×103 5.5×102

TOTAL 3.1×103 6.0×102

Since the energy distribution of the background gamma flux is unknown it

is almost impossible to predict the semiconductor detector charge saturation. The

read-out rate of the recently developed detector system is limited by 100 kHz. At

the same time, the useful events rate under the typical experimental conditions

does not usually exceed the 10 kHz level. Therefore, in the extreme case of 100 %

microstrip detector efficiency for the background radiation a signal-to-noise ratio is

estimated to be about 3101.3101 34 ≈×× , which is just enough to extract relevant

physical information from the data. In reality this ratio is expected to be much

higher because of the trigger detector used for preventing the silicon detector from

registration of other events than those from electrons by means of active

background suppression.

40

6. Construction of the shielding

In the framework of this diploma thesis the new shielding has been

designed. The shielding was constructed two-layered. The protection against

photons is achieved by a 10 cm inner layer of lead bricks. The shield against

neutrons consists of an outer layer of 20 cm borated polyethylene plates.

Since the total weight exceeds the limit of 5 tons, the lead shielding

consists of four separated sidewalls and a cover. The dimensions have been chosen

to provide some free space between the lead shielding and the detector system in

order to allow future modifications of the detector system. The lead walls are built

from standard bricks (200mm × 100mm × 50mm) held together by U-steel frames

shown in Fig. 14.

7 .5

7.5

1 2 0

1 0 0

110

Fig. 14: Dimensions of a U-steel frame for supporting lead bricks in mm.

Drawings of the individual parts are shown in Fig. 15. The backside wall

will be installed permanently to allow a fixed placement of the necessary detector

cables. The other walls and the cover will be removable.

41

Front Wall

1 0 15

1015

Cover

1 3 6 5

1015

Side Walls (2 pieces)

11 1 5

1015

Back Wall

1 015 1 5 0

4 0 0

1 0 1 5

250

600

Fig. 15: Drawings of the individual U-steel frames for the lead shielding.

All dimensions in mm.

A three-dimensional view of the lead shielding is shown in Fig. 16. The

steel strips which are also shown in the figure are necessary as an additional side

support for the lead bricks. The sidewalls are connected with each other by means

of iron angle.

42

Front Wall

Lead bricks

Steel strips supporting

lead bricksSide Walls

U-steel frame

Back Wall

Cover

Fig. 16: Three-dimensional view of the new lead shielding.

The required amount of lead bricks for each piece and their total weight are

given in Tab. 8. In total 540 lead bricks are needed. The lead shielding is

surrounded with 20 cm borated polyethylene plates for the shielding against

neutron. Their total weight is about 830 kg.

Tab. 8: Required amount of lead bricks for each piece and their total weight.

Required amount of bricks Weight of the wall [kg]

Side walls (2) 110 × 2 = 220 1247.4 × 2

Front wall 100 1134

Back wall ≈ 85 963.9

Cover 135 1530.9

Total 540 6123.6

43

7. Conclusion

In the framework of this diploma thesis a new passive shielding against

neutrons and ionizing radiation produced by neighbouring background sources was

designed for the detector system of the energy-loss spectrometer at the

S-DALINAC. Estimates of the total background yields produced by the most

important background sources like the 70° bending magnet, the target and the post-

target system were presented. Based on these estimates and taking into account that

the new shielding should attenuate the background down to a level at which the

new detector system can operate properly the new shielding was designed.

Furthermore, the construction enables a simple assembling and disassembling to

provide an easy access to the detectors.

Estimates of the shielding thickness were carried out using experimentally

measured shielding TVL parameters. The designed shielding consists of an inner

10 cm thick lead brick layer and an outer 20 cm thick borated polyethylene. The

lead bricks walls are constructed using U-steel frames.

The shielding is currently under construction in the mechanical workshop

and will be ready for use as soon as it is finished.

44

8. References

[1] A. Richter, Prog. Part. Nucl. Phys. 44 (2000) 3.

[2] P. von Neumann-Cosel, F. Neumeyer, S. Nishizaki, V. Yu. Ponomarev, C.

Rangacharyulu, B. Reitz, A. Richter, G. Schrieder, D. I. Sober, T.

Waindzoch, and J. Wambach, Phys. Rev. Lett. 82 (1999) 1105.

[3] S. Strauch, P. von Neumann-Cosel, C. Rangacharyulu, A. Richter,

G. Schrieder, K. Schweda and J. Wambach, Phys. Rev. Lett. 85 (2000)

2913.

[4] H.-D. Gräf, H. Miska, E. Spamer, O. Titze, and T. Walcher, Nucl. Instr.

Meth. 153 (1978) 9.

[5] T. Walcher, R. Frey, H.-D. Gräf, E. Spamer and H. Theissen, Nucl. Instr.

Meth. 153 (1978) 17.

[6] D. Schüll, J. Foh, H.-D. Gräf, H. Miska, R. Schneider, E. Spamer,

H. Theissen, 0. Titze and T. Walcher, Nucl. Instr. Meth. 153 (1978) 29.

[7] J. Foh, R. Frey, R. Schneider, A. Schwierczinski, H. Theissen and 0. Titze,

Nucl. Instr. Meth. 153 (1978) 43.

[8] A. Lenhardt, Diplomarbeit, TU Darmstadt (1999).

[9] A. Richter, Proceedings of the Fifth European Particle Accelerator

Conference, ed. S. Meyers et al., (IOP Publishing, Bristol, 1996) 110.

[10] J.C. Butcher and H. Messer, Nucl. Phys. 20 (1960) 15.

[11] O.V. Bogdankevich, Methods in Bremsstrahlung Research (Academic Press,

London, 1966).

[12] W.R. Leo, Techniques for Nuclear and Particle Physics Experiment

(Springer-Verlag Berlin Heidelberg, 1994).

[13] Review of Particle Properties in Phys. Rev. D45 , Part II (1992).

[14] L.I. Schiff, Phys.Rev. 83 (1951) 252.

[15] ICRU Report 37 (1984).

[16] W. Miller, R.J. Kennedy, Radiat. Res. 4 (1956) 360.

45

[17] D.A. Scag, Discussion of radiographic characteristic of high-energy X-rays,

Nondestr. Test 12 (1954) 47.

[18] K. Shure, J.A. O’Brien, D.M. Rothberg, Nucl. Sci. Eng. 35 (1969) 371.

[19] S.S. Dietrich and B.L. Berman, Atomic Data and Nuclear Tables 38 (1988)

199.

[20] M. E. Toms and W. E. Stephens, Phys. Rev. 108 (1957) 77.

[21] S. Oki, Y. Takashima, M. Yamakage, H. Kibayakawa, K. Yoshida, K. Goto,

Proceedings of the Second International Workshop on EGS, 8.-12. August

2000, Tsukuba, Japan, pp. 293-298.

[22] W.P. Swanson, Radiological Safety Aspects of the Operation of Electron

Linear Accelerators, IAEA Technical Report Series No. 188 (1979).

[23] S. Kowalski, H.A. Enge, RAYTRACE User’s Guide, Laboratory for Nuclear

Science and Department of Physics, MIT, (1986).

[24] T. Walcher, Habilitationsschrift, TH Darmstadt (1974).

[25] Y. Kalmykov, private communication.

[26] H. Dinter and K. Tesch, Deutsches Elektronen Synchrotron, Hamburg,

Rep. DESY-76/19 (1976).

[27] M. Knirsch, Dissertation, TH Darmstadt (1991), D-17.

46

Acknowledgements

At this place I would like to thank several people who have contributed to

the success of this work.

On the first place I would like to sincerely thank Professor Dr. Dr. h.c.

mult. Achim Richter for given great opportunity to work on such an exciting topic

under his supervision and to sense the climate of constructive team work in the

modern scientific laboratory.

Further on I would like to thank Privatdozent Dr. Peter von Neumann-

Cosel for numerous useful discussions during the realization of this diploma thesis

and for the valuable remarks which he has made during the reading of this thesis.

I address my heartful gratitude to Dr. Harald Genz for his every day help,

care and support.

I am greatful to Dipl.-Phys. Alexander Lenhardt for introducing me to the

topic, his qualified and friendly patronage and for critical reading of this thesis.

I would like to express my gratitude also to Dipl.-Phys. Yaroslav

Kalmykov, Dipl.-Phys. Sergiy Khodyachykh, and Dipl.-Phys. Artem Shevchenko for

numerous significant advices.

I am grateful to Dr. Shmatko, Dr. Shchus and Chair of the Experimental

Nuclear Physics of the Karazin Kharkiv National University (Ukraine) for the time

they have spent for my education.

Mrs. Sabine Genz I would like to thank for the time she has spent on

improving my English.

My special thank goes to the family Hartmann. Their warm and friendly

attitude towards me helped me to feel at home here in Germany.

Finally, my heartful gratitude to my family – my parents Mykola and

Tetyana and my sister Julia. Your thoughts and your care were supporting me very

much during my study in the Karazin Kharkiv National University and during stay

in Darmstadt.